Newton's Third Law

Forces
principle

Also known as: action-reaction, N3

Grade 9-12

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For every action force, there is an equal in magnitude and opposite in direction reaction force. Newton's third law explains how rockets propel themselves in the vacuum of space, how you can walk by pushing backward on the ground, and why every interaction in nature involves mutual forces.

Definition

For every action force, there is an equal in magnitude and opposite in direction reaction force.

💡 Intuition

When you push something, it pushes back on you just as hard.

🎯 Core Idea

Forces always come in paired interactions — each force has a matching opposite force on the other object.

Example

You push off the ground to jump; the ground pushes you upward.

Notation

\vec{F}_{A \to B} denotes the force exerted by object A on object B. The negative sign indicates that \vec{F}_{B \to A} points in the opposite direction. Both forces have the same magnitude |\vec{F}| in newtons.

🌟 Why It Matters

Newton's third law explains how rockets propel themselves in the vacuum of space, how you can walk by pushing backward on the ground, and why every interaction in nature involves mutual forces.

💭 Hint When Stuck

When applying Newton's third law, first identify the two interacting objects. Then name both the action force and reaction force, specifying which object each acts on. Finally, remember that the two forces are equal in magnitude, opposite in direction, and act on different objects — they never cancel each other.

Formal View

If object A exerts a force \vec{F}_{A \to B} on object B, then B simultaneously exerts a force \vec{F}_{B \to A} = -\vec{F}_{A \to B} on A. The forces are equal in magnitude, opposite in direction, and act on different bodies.

🚧 Common Stuck Point

The action and reaction forces act on DIFFERENT objects, so they don't cancel out.

⚠️ Common Mistakes

  • Thinking action and reaction forces cancel out — they act on different objects, so they cannot cancel.
  • Confusing a Newton's third law pair with two forces on the same object (like weight and normal force on a book, which are NOT a third-law pair).
  • Believing that the 'reaction' happens after the 'action' — both forces exist simultaneously and are always equal.

Frequently Asked Questions

What is Newton's Third Law in Physics?

For every action force, there is an equal in magnitude and opposite in direction reaction force.

When do you use Newton's Third Law?

When applying Newton's third law, first identify the two interacting objects. Then name both the action force and reaction force, specifying which object each acts on. Finally, remember that the two forces are equal in magnitude, opposite in direction, and act on different objects — they never cancel each other.

What do students usually get wrong about Newton's Third Law?

The action and reaction forces act on DIFFERENT objects, so they don't cancel out.

Next Steps

momentumimpulse

How Newton's Third Law Connects to Other Ideas

To understand newton's third law, you should first be comfortable with force and newtons first law. Once you have a solid grasp of newton's third law, you can move on to momentum and impulse.

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